Tyson, the biggest U.S. meat processor by sales, told cattle suppliers in a letter Wednesday that it would stop buying cattle given Merck & Co.’s Zilmax—which promotes weight gain—after receiving animals at some of its beef plants that had difficulty walking or were unable to move.

Merck spokeswoman Pam Eisele said the company’s data “do not support Zilmax as being the cause of these issues” and that “we remain confident in the safety of the product.”

She said Merck is offering assistance to Tyson in identifying the cause of the problems. Zilmax has been sold commercially in global markets since the mid-1990s and was approved by the Food and Drug Administration for cattle in 2006, she said.

The news fueled speculation that U.S. beef supplies could decline as cattle weights drop due to Tyson’s action.

Zilmax, fed to cattle in the final weeks before slaughter, can add about 2%, or 24 to 33 pounds, to an animal’s weight. Tyson accounts for roughly a quarter of the daily slaughter of cattle in the U.S.

Live cattle for October delivery, the most-active contract at the Chicago Mercantile Exchange, initially climbed the daily limit of 3 cents a pound Thursday, before settling up 2.4 cents, or 1.9%, at $1.2707 a pound. Live cattle for August delivery gained 1.45 cents, or 1.2%, to $1.2267, the highest closing price for the front-month contract since July 9.

Prices retreated slightly early Friday as some traders took profits.

Analysts said Tyson’s move could lead to somewhat higher beef prices in coming months for U.S. consumers. Any increase in beef prices could be felt acutely in the supermarket, where consumers already face near-record beef prices because U.S. cattle supplies have tightened in the past few years due to a long drought in Texas and other big cattle-producing states. Retail beef prices jumped 6.4% last year and are expected to rise further this year, as the U.S. cattle herd shrank to its smallest level in six decades, according to the U.S. Department of Agriculture.

But analysts said the impact should be limited unless other major meatpackers impose similar bans. Any increase in beef prices also likely will be tempered by recent declines in the price of corn, the main ingredient in livestock feed, amid expectations for a big U.S. corn crop this fall. Some of Tyson’s cattle suppliers that use Zilmax also are expected to switch to a competing product like Optaflexx, mitigating the impact on supplies, analysts said. Optaflexx is made by Eli Lilly & Co.’s Elanco unit.

Cargill Inc., another major U.S. beef processor, said it would continue to buy cattle fed with Zilmax, a practice it began last year. Two other major U.S. beef packers—JBS SA and National Beef Packing Co.—didn’t respond to requests for comment.

Feedlots, which buy young cattle from ranchers and fatten them for slaughter over four to six months, could face tighter profit margins if they can’t use Zilmax. While they can switch to Optaflexx, that additive provides somewhat lower weight gain. Feedlots could have to buy more corn to fatten cattle or sell animals at lower weights.

Still, some feedlot operators say they have mixed feelings about Zilmax. Steve Landgraf, co-owner and manager of Lakin Feed Yard in Lakin, Kan., said it had helped his cattle gain weight, but he stopped using the supplement earlier this year because he found it changed the behavior of his animals.

Some cattle fed with Zilmax “get mean and don’t want to be handled,” Mr. Landgraf said. He added: “I’ll admit it works.”

Rich Nelson, chief strategist at Allendale Inc., a brokerage in McHenry, Ill. estimated U.S. beef production would drop 0.4% if Tyson is the only beef packer that bans Zilmax, and Optaflexx remains in use. He doesn’t expect other meatpackers to follow Tyson’s lead unless the company bans other feed additives as well.

The move by Tyson, based in Springdale, Ark., casts a new spotlight on the use of feed supplements to help livestock grow faster. Zilmax has gained popularity in recent years as beef producers grappling with high grain prices and drought have sought to raise animals more economically. Merck estimates that about 70% of the U.S. beef industry’s cattle supply is fed with Zilmax or Optaflexx.

Tyson told suppliers it would suspend purchases of cattle fed with Zilmax effective Sept. 6 while it continues to evaluate why some of the animals it had received were unable to move or to walk. “We do not know the specific cause of these problems, but some animal health experts have suggested” the use of Zilmax, Tyson said in its letter. “This is not a food safety issue,” the company added, but “about animal well-being.”

Groups like the Animal Legal Defense Fund and the Center for Food Safety have criticized the use of Zilmax and other growth-promoting agents, saying the drugs need further study.